In various fields of solid mechanics and engineering it is essential to describe contact and friction between two bodies.
This is the case, e.g., when modelling foundations and joints in buildings or when considering impact problems.
In this paper, we focus on a simplified unilateral contact problem without friction, for which contact is mathematically expressed by some inequalities and complementarity conditions.
These constraints translate non-penetration as well as the absence of cohesive forces and friction between the two bodies.
In order to deal with the above constraints from a numerical point of view, different strategies have been proposed in the literature, including penalized formulations, mixed formulations, and weak enforcement à la Nitsche.
We focus on the latter, which does not require the introduction of Lagrange multipliers and results in a coercive formulation that is easy to implement.
The literature on the numerical approximation of contact problems is vast, and a comprehensive state-of-the-art lies outside of the scope of the present papers.
We refer to the review articles [1]}, [2]} and references therein for a broader discussion.
